4: Acoustics

Example number 4.1, Page number 24

In [3]:
#importing modules
import math
from __future__ import division
import numpy as np

#Variable declaration
I1=10**-12;   #intensity(W/m**2)
I2=0.1;   #intensity of sound(W/m**2)

#Calculation
beta=10*np.log10(I2/I1);   #intensity level(dB) 

#Result
print "intensity level is",beta,"dB"

intensity level is 110.0 dB

Example number 4.2, Page number 24

In [6]:
#importing modules
import math
from __future__ import division
import numpy as np

#Variable declaration
I1=10**-12;   #intensity(W/m**2)
I2=10**-4;   #intensity of sound(W/m**2)

#Calculation
beta=10*np.log10(I2/I1);   #relative sound intensity(dB) 

#Result
print "relative sound intensity is",beta,"dB"

relative sound intensity is 80.0 dB

Example number 4.3, Page number 25

In [10]:
#importing modules
import math
from __future__ import division
import numpy as np

#Variable declaration
I2byI1=2;    #intensity ratio

#Calculation
beta=10*np.log10(I2byI1);   #increase in sound intensity level(dB) 

#Result
print "increase in sound intensity level is",round(beta,2),"dB"

increase in sound intensity level is 3.01 dB

Example number 4.4, Page number 25

In [13]:
#importing modules
import math
from __future__ import division
import numpy as np

#Variable declaration
P=3.14;   #power radiated(W)
r=10;   #radius(m)
I11=100;  #intensity(W/m**2)
I12=1;   #intensity(W/m**2)
I13=10**-12;  #intensity(W/m**2)

#Calculation
I2=P/(4*math.pi*r**2);   #intensity of sound(W/m**2)
beta1=10*np.log10(I2/I11);   #relative intensity(dB) 
beta2=10*np.log10(I2/I12);   #relative intensity(dB) 
beta3=10*np.log10(I2/I13);   #relative intensity(dB) 

#Result
print "relative intensity with respect to 100W/m**2 is",round(beta1,4),"dB"
print "relative intensity with respect to 1W/m**2 is",round(beta2,4),"dB"
print "relative intensity with respect to 10**-12W/m**2 is",round(beta3,3),"dB"

relative intensity with respect to 100W/m**2 is -46.0228 dB
relative intensity with respect to 1W/m**2 is -26.0228 dB
relative intensity with respect to 10**-12W/m**2 is 93.977 dB

Example number 4.5, Page number 26

In [15]:
#importing modules
import math
from __future__ import division
import numpy as np

#Variable declaration
P=1.5;   #power radiated(J/s)
r=20;   #radius(m)
I1=10**-12;  #intensity level of sound(W/m**2)

#Calculation
I2=P/(4*math.pi*r**2);   #intensity of sound(W/m**2)
beta=10*np.log10(I2/I1);   #intensity level(dB) 

#Result
print "intensity level of sound is",round(beta,1),"dB"

intensity level of sound is 84.7 dB

Example number 4.6, Page number 27

In [16]:
#importing modules
import math
from __future__ import division

#Variable declaration
beta1=80;   #intensity level of sound(dB)

#Calculation


#Result
print " "

Example number 4.7, Page number 28

In [17]:
#importing modules
import math
from __future__ import division

#Variable declaration
V=1500;   #volume of hall(m**3)
sigma_a1s=100;   #absorption of sound by hall(sabine)
sigma_a2s=100;   #absorption of sound by audience(sabine)

#Calculation
A=sigma_a1s+sigma_a2s;   #total absorption(sabine)
t1=0.16*V/sigma_a1s;   #reverberation time of hall when room is empty(s)
t2=0.16*V/(sigma_a1s+sigma_a2s);   #reverberation time of hall when room is filled(s)
t=t1-t2;   #change in reverberation time(s)

#Result
print "when the room is filled, reverberation time is reduced to",t,"s"

when the room is filled, reverberation time is reduced to 1.2 s

Example number 4.8, Page number 28

In [19]:
#importing modules
import math
from __future__ import division

#Variable declaration
V=1000;   #volume of hall(m**3)
T=2;   #reverberation time(s)
s=350;   #area of sound absorbing surface(m**2)

#Calculation
alpha=0.16*V/(T*s);   #average absorption coefficient

#Result
print "average absorption coefficient is",round(alpha,5)

average absorption coefficient is 0.22857

Example number 4.9, Page number 29

In [23]:
#importing modules
import math
from __future__ import division

#Variable declaration
V=2400;   #volume of hall(m**3)
a1=500;   #area of plaster ceiling(m**2)
s1=0.02;  #coefficient of absorption of plaster ceiling
a2=600;   #area of plaster walls(m**2)
s2=0.03;  #coefficient of absorption of plaster walls
a3=500;   #area of wood floor(m**2)
s3=0.06;  #coefficient of absorption of wood floor
a4=20;    #area of wood doors(m**2)
s4=0.06;  #coefficient of absorption of wood doors
a5=400;   #area of cushion seats(m**2)
s5=0.01;  #coefficient of absorption of cushion seats
a6=200;   #area of cane seats(m**2)
s6=0.01;  #coefficient of absorption of cane seats 
s=0.45;   #absorption of each member(sabine)

#Calculation
sigma_asE=(a1*s1)+(a2*s2)+(a3*s3)+(a4*s4)+(a5*s5)+(a6*s6);   #total absorption when hall is empty(sabine)
TE=0.16*V/sigma_asE;   #reverberation time when hall is empty(s)
sigma_asF=(a1*s1)+(a2*s2)+(a3*s3)+(a4*s4)+(a5*s)+(a6*s);    #total absorption when hall is filled(sabine)
TF=0.16*V/sigma_asF;   #reverberation time when hall is filled(s)

#Result
print "reverberation time when hall is empty is",round(TE,4),"s"
print "reverberation time when hall is filled is",round(TF,3),"s"

reverberation time when hall is empty is 5.8896 s
reverberation time when hall is filled is 1.166 s

Example number 4.10, Page number 30

In [25]:
#importing modules
import math
from __future__ import division
import numpy as np

#Variable declaration
I1=10**-12;   #intensity(W/m**2)
I2=100;   #intensity of sound(W/m**2)

#Calculation
beta=10*np.log10(I2/I1);   #intensity level of jet plane(dB) 

#Result
print "intensity level of jet plane is",beta,"dB"

intensity level of jet plane is 140.0 dB